The Japan Rail Pass math question comes up constantly, so I'm going to work through it for a specific itinerary.

My 14-day trip covered Tokyo → Kyoto → Osaka → Hiroshima → Naoshima Island → Tokyo. The 14-day JR Pass costs ¥50,000 ($330 at current rates).

Point-to-point Shinkansen fares for my route: Tokyo-Kyoto ¥13,910, Kyoto-Osaka ¥1,420 (local train, not covered anyway), Osaka-Hiroshima ¥9,440, Hiroshima-Okayama ¥3,270 (for Naoshima ferry), Okayama-Tokyo ¥17,340. Total: ¥45,380 ($300).

So the pass came out slightly more expensive than point-to-point for my specific route — but I also used it for metro rides in Tokyo (some lines), the Narita Express airport transfer, and several regional trains I took on a whim without planning. Once I factor those in, it broke roughly even, with the added value of not having to queue at ticket machines or plan every leg.

Verdict: the pass makes sense if your itinerary is Shinkansen-heavy and covers 500+ km between major cities. If you're mostly staying in one region or using local transit, skip it and buy as you go via IC cards (Suica/Pasmo).